Question

What is the missing term in the factorization? 100x^2−36=4(5x+?)(5x−3)

Answer 1

To get the missing terms, we must completely factorize the Left Hand Side of the Equation.

We can do this in two different ways

Method 1

$100x^{2} -36= 4(25x^{2} -9)}$

$\Rightarrow 100x^{2} -36= 4((5x)^{2} -3^2)}$

Using difference of two squares we have

$\Rightarrow 100x^{2} -36= 4(5x+3)(5x-3)}$

By comparing to the given equation, the missing term is

$3$

Method 2

$100x^{2} -36$

$\Rightarrow 100x^{2} -36= (10x)^{2} -6^{2}$

Recall and apply the difference of two squares formula, to obtain,

$100x^{2} -36=(10x+6)(10x-6)$

We can still further factor 2 out of each factor to get,

$100x^{2} -36=2(5x+3) \times 2(5x-3)$

$\Rightarrow 100x^{2} -36=2\times2(5x+3)(5x-3)$

$\Rightarrow 100x^{2} -36=4(5x+3)(5x-3)$

By comparing to the given equation, the missing term is

$3$

Answer 2

100x^2−36=4(5x+3)(5x−3)